Question

$\text{Factorise:}{a}^4+4a^2{b}^2+4b^4$

• A. $(a^2+2b^2{)}^2$
• B. $(a^2-2b^2{)}^2$
• C. $(2a^2+b^2{)}^2$
• D. $(2a^2-b^2{)}^2$

Answer 1

The correct option is A $(a^2+2b^2{)}^2$

$\text{Given:}{a}^4+4a^2{b}^2+4b^4$

$a^4+4a^2{b}^2+4b^4$ $=(a^2{)}^2+4a^2{b}^2+(2b^2{)}^2$
$=(a^2{)}^2+2(a^2\left)\right(2b^2)+(2b^2{)}^2$

$\text{This is in the form of}{a}^2+2ab+b^2\text{where,}a=a^2\text{and}b=2b^2.$

$\text{Using the identity}(a+b{)}^2=a^2+2ab+b^2,\text{we get}{a}^4+4a^2{b}^2+4b^4=(a^2+2b^2{)}^2$

$\text{Hence,}{a}^4+4a^2{b}^2+4b^4=(a^2+2b^2{)}^2.$